Answer:
a) 17.5
b) 15.6
c) 13.3
d) 21.51
Step-by-step explanation:
The given function is equal to:
f(x)=kx^2
where
![\int\limits^y_0 {kx^{2} } \, =1](https://tex.z-dn.net/?f=%5Cint%5Climits%5Ey_0%20%7Bkx%5E%7B2%7D%20%7D%20%5C%2C%20%3D1)
where y=23
Clearing k=0.00025
a) ![Ex=\int\limits^y_0 {xf(x)} \, dx =\int\limits^y_0 {x*0.00025x^{2} } \, dx =17.5](https://tex.z-dn.net/?f=Ex%3D%5Cint%5Climits%5Ey_0%20%7Bxf%28x%29%7D%20%5C%2C%20dx%20%3D%5Cint%5Climits%5Ey_0%20%7Bx%2A0.00025x%5E%7B2%7D%20%7D%20%5C%2C%20dx%20%3D17.5)
b)![Vx=Ex^{2} -(Ex)^{2} =\int\limits^y_0 {x^{2}f(x) } \, dx-17.5^{2} =\int\limits^y_0 {x^{2} *0.00025x^{2} } \, dx -17.5^{2} =321.82-306.25=15.6](https://tex.z-dn.net/?f=Vx%3DEx%5E%7B2%7D%20-%28Ex%29%5E%7B2%7D%20%3D%5Cint%5Climits%5Ey_0%20%7Bx%5E%7B2%7Df%28x%29%20%7D%20%5C%2C%20dx-17.5%5E%7B2%7D%20%20%3D%5Cint%5Climits%5Ey_0%20%7Bx%5E%7B2%7D%20%2A0.00025x%5E%7B2%7D%20%7D%20%5C%2C%20dx%20-17.5%5E%7B2%7D%20%3D321.82-306.25%3D15.6)
c) The function is equal to:
f(x)=k(1+2x)
![\int\limits^y_0 {k(1+2x)} \, =1](https://tex.z-dn.net/?f=%5Cint%5Climits%5Ey_0%20%7Bk%281%2B2x%29%7D%20%5C%2C%20%3D1)
where y=20
k=0.0024
![Ex=\int\limits^y_0 {xf(x)} \, dx =\int\limits^y_0 {x*0.0024(1+2x)} \, dx =13.3](https://tex.z-dn.net/?f=Ex%3D%5Cint%5Climits%5Ey_0%20%7Bxf%28x%29%7D%20%5C%2C%20dx%20%3D%5Cint%5Climits%5Ey_0%20%7Bx%2A0.0024%281%2B2x%29%7D%20%5C%2C%20dx%20%3D13.3)
d) ![Vx=Ex^{2} -(Ex)^{2} =\int\limits^y_0 {x^{2} f(x)} \, dx -13.3^{2}=\int\limits^y_0 {x^{2} *0.0024(1+2x)} \, dx-13.3^{2} =198.4-176.89=21.51](https://tex.z-dn.net/?f=Vx%3DEx%5E%7B2%7D%20-%28Ex%29%5E%7B2%7D%20%3D%5Cint%5Climits%5Ey_0%20%7Bx%5E%7B2%7D%20f%28x%29%7D%20%5C%2C%20dx%20-13.3%5E%7B2%7D%3D%5Cint%5Climits%5Ey_0%20%7Bx%5E%7B2%7D%20%2A0.0024%281%2B2x%29%7D%20%5C%2C%20dx-13.3%5E%7B2%7D%20%20%20%3D198.4-176.89%3D21.51)
A.
To get dividend per share, we need to divide total dividend by total numbers of shares outstanding.
Dividend per share =
dollars.
B.
Since per share you get $0.8, for 100 shares you will get
dollars.
Also, that is
percent of the total dividends.
ANSWER:
A. $0.8 per share
B. $80 (and that is 0.2% of total dividend)
Answer:
1. a. 3xy²(7x²y³ + 5x - 4y)
2. a. (3x + 2)(5x + y)
3. d. (2a + b)(5x - 4)
Step-by-step explanation:
For #1, your answer was missing an exponent, which I boldfaced. Every term has a <em>y</em><em>²</em><em> </em>in common. Then, in numbers 2 and 3, just factor each group one at a time.
Ex: [10ax + 5bx] - [8ay - 4by]
Answer:
![P(\bar X< 651.1) =P(\bar X< \frac{651.1-651.25}{\frac{0.73}{\sqrt{78}}}= -1.815](https://tex.z-dn.net/?f=P%28%5Cbar%20X%3C%20651.1%29%20%3DP%28%5Cbar%20X%3C%20%5Cfrac%7B651.1-651.25%7D%7B%5Cfrac%7B0.73%7D%7B%5Csqrt%7B78%7D%7D%7D%3D%20-1.815)
And using the normal atandard table or excel we got:
![P(z](https://tex.z-dn.net/?f=%20P%28z%3C-1.815%29%20%3D%200.0348)
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
Solution to the problem
Let X the random variable that represent the length of the tape of a population, and for this case we know the following parameters
Where
and
We sselect a sample size of n =78>30. From the central limit theorem we know that the distribution for the sample mean
is given by:
And we want to find this probability:
![P(\bar X< 651.1) =P(\bar X< \frac{651.1-651.25}{\frac{0.73}{\sqrt{78}}}= -1.815](https://tex.z-dn.net/?f=P%28%5Cbar%20X%3C%20651.1%29%20%3DP%28%5Cbar%20X%3C%20%5Cfrac%7B651.1-651.25%7D%7B%5Cfrac%7B0.73%7D%7B%5Csqrt%7B78%7D%7D%7D%3D%20-1.815)
And using the normal atandard table or excel we got:
![P(z](https://tex.z-dn.net/?f=%20P%28z%3C-1.815%29%20%3D%200.0348)
I think it was for 2.33 cents??